Magic squares, are squares containing different numbers, of which the sum of the numbers in each row, in each column and in both diagonals always yield the magical constant. In my magical page you can create magic squares of 3× 3 to 99× 99. Only one solution of the often countless solutions is calculated, but you can make them visible in 8 ways. You can save the magic squares in a file that can be read directly by spreadsheet programs.
Go to the magical page. Go to the page wih special magic squares Or: go to this unique magic cryptograms page!
Pascal Triangle
There's much to say about this very useful triangle. However, I only have a simulation that shows which numbers can be divided by a given divisor.
My smart 14-year-old high school girls
I have been teaching math to some very bright girls. The twin sisters Ariella and Briella claim that together they can find the root of any square number between 100 and 10000 within one second. See here how they do it.
My smart 15-year-old high school girls
I have been fortunate enough to teach math to seven bright girls.
These girls can add two numbers together without either of them knowing which numbers those are. This is a mathematics/computer science story. Read it here.
My smart 16-year-old high school girls
The 10th grade girls of last year all graduated. This year they have a little riddle for you... Find out which mathematical figure they draw on the schoolyard.
Read the story and play the simulation!
The bright minds of my HAVO final exam class
The smart final exam students will always win my challenge, with a little help from the teaching assistant. Read about it here.
Pentomions are figures made up of five squares. Those five pieces are joined by at least one side. There are 12 possible shapes, if you don't count mirrored shapes. There are also pentomino calendars for sale. These have seven different pentomino pieces. The idea is to place six of these so that all the numbers are covered except the current day. So you have to solve a puzzle every day. You may rotate the pieces and also flip them (so that you get the mirrored shape), but they must not overlap. Below you can see a possible solution for July 10th and also how all seven pieces fit into the box.
Solve the calendar with the following pentomino pieces:
If you follow this link you can see a solution for today and other days, but.... try it yourself first! There are different solutions every day.
If you want to make it more difficult for yourself, you can try to solve the puzzle using only these pentomino pieces:
If you follow this link you can see a solution for today and other days, but.... try it yourself first! There are different solutions every day.
Divide by 11
If you want to know how to easily find out if a number is divisible by 11 or if you want to know an easy method to divide by 11, read on here.
There is a basket of eggs in the farm shop. It says, "These eggs were laid today. They cost 14 cents each."
A customer said, "Give me half of all the eggs in the basket plus half an egg." The farmer put this neatly in an egg carton and the customer paid. The next customer said, "Give me half of all the eggs in the basket plus half an egg." The farmer put this neatly in an egg carton and the customer paid. Finally, a third customer arrived. She said, "May I have half of all the eggs in the basket plus half an egg."
"Sure", said the farmer and after the customer had paid he put the empty basket away.
The question now is: how much money did the three customers pay together.
Mirror number
If you take a random number and put the same number mirrored before (or after) then I call that a mirror number. An example is 12344321. A mirror number is always divisible by 11. Try this yourself below
Enter a number here:
A mirror number is also a palindromic number: that is a number that stays the same when you read it backwards. However, a palindromic number is not always a mirror number. For example, 121 is a palindromic number, but not a mirror number, because the 2 is not repeated.
Who's birthday is today? Only the teacher knows who is having a birthday. Still, the birthday student gets a dollar from all the classmates. Click here.
Horse jump word puzzles
Have you ever tried solving a so-called horse jump word puzzle? Although large puzzles are also possible, the 3 by 3 variant is the best known. One possible strategy is to try to find word patterns, but if you have a lot of identical letters that can be tricky.
Yet the word can be found quickly, because there are only 16 possibilities. So it is very well possible to find the solution by systematically going through all the possibilities. Start at the top left and follow the eight possibilities in a clockwise direction and then in a counterclockwise direction. Usually after a few letters you already know whether a word is possible or not. If there are two of you, you can decide that one will try the 8 anti-clockwise solutions and the other the clockwise solution. After 8 attempts you will definitely have the solution. I have put a page here that shows all the possibilities of any eight-letter word. Normally you use either uppercase or lowercase letters only, but the program doesn't force that.
Probabilities
In general, people are very bad at estimating probabilities. Fortunately, mathematics can often help. The birthday paradox described above is an example of this.
The Monty Hall problem
This famous problem is an example of a result that feels counterintuitive for many, many people. Still to be done.
Winning dice
How to win a gambling game often with your own fair dice? Read it here.
Solve the calendar with the following pentomino pieces:
